# Full text of "Analytical Mechanics"

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```EQUILIBRIUM OF FLEXIBLE CORDS
Dividing equation (4) by the last equation we get
or                                          P=Iloge2
Thus if 6 - nP, then by equations (4) and (5)
rp _   TO t
71
(5)
(6)
Therefore taking 0.53 for hemp rope on oak and 9 = 2 TT, we obtain n = 4.76 and 2n = 27.3. Hence in this case TQ is 27.3 times as great as T.
APPLICATION TO BELTS. — The tensile force on one side of a belt which transmits power is greater than that on the other side. The relation between the tensile forces on the: two sides of the belt is given by equation (4). Thus if Tr denotes the tensile force on the driving side and T2 that on the slack side, then
ft = T&-*  or    Ti = T^.                    (40'
The difference between T\ and T2 is the effective force which drives the pulley. Denoting the effective force by F, we have
F = Ti - T2
= Ti (1 -
(7)
We have neglected the cross-section of the cord in the solution of the foregoing problem. Therefore the results which we have obtained are applicable to actual problems only when the cross-section of the cord is negligible compared with that of the solid with which it is in contact.```